Two angles are supplementary if their measures add up to 180 degrees. Given the measures of the angles:
- m<QRS = x + 40
- m<SRT = x
We can set up the equation:
\[ m<QRS + m<SRT = 180 \]
Substituting the expressions for the angles:
\[ (x + 40) + x = 180 \]
Combining like terms:
\[ 2x + 40 = 180 \]
Subtracting 40 from both sides:
\[ 2x = 140 \]
Dividing by 2:
\[ x = 70 \]
Now, we can find the measure of angle <QRS:
\[ m<QRS = x + 40 = 70 + 40 = 110 \]
Therefore, the measure of <QRS is:
\[ \boxed{110} \]